How do you solve the following system?: $9 y = - 3 x - 9, 5 x + 3 y = - 3$ $9y = -3x - 9 , 5x + 3y = -3$

Question

2113 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-07T14:28:04

Substitution/Elimination/Graphing Method

Using the substitution method, starting with the first equation:

$9 y = - 3 x - 9$ $9y = -3x-9$

$9 y + 9 = - 3 x$ $9y+9 = -3x$

$\frac{9 y}{- 3} + \frac{9}{- 3} = \frac{- 3 x}{- 3}$ $(9y)/-3+9/-3 = (-3x)/-3$

$x = - 3 y - 3$ $x = -3y -3$

Substituting $(x = - 3 y - 3)$ $(x=-3y-3)$ into the second equation to find $y$ $y$ :

$5 x + 3 y = - 3$ $5x+3y = -3$

$5 (- 3 y - 3) + 3 y = - 3$ $5(-3y-3) + 3y=-3$

$- 15 y - 15 + 3 y = - 3$ $-15y-15 + 3y=-3$

$- 12 y = 12$ $-12y=12$

$y = - 1$ $y=-1$

Now substituting $(y = - 1)$ $(y=-1)$ into second equation to find $x$ $x$ :

$5 x + 3 y = - 3$ $5x+3y = -3$

$5 x + 3 (- 1) = - 3$ $5x+3(-1)=-3$

$5 x - 3 = - 3$ $5x-3 = -3$

$5 x = 0$ $5x= 0$

$x = 0$ $x =0$

Test $(x = 0, y = - 1)$ $(x=0, y=-1)$ in other equation to validate

$9 y = - 3 x - 9$ $9y = -3x-9$

$9 (- 1) = - 3 (0) - 9$ $9(-1) = -3(0)-9$

$- 9 = - 9$ $-9 = -9$ ,

How do you solve the following system?: 9y = -3x - 9 , 5x + 3y = -3 9y=−3x−9,5x+3y=−39y = -3x - 9 , 5x + 3y = -3